On non-uniqueness of mild solutions and stationary singular solutions to the Navier-Stokes equations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908865285586944 |
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| author | Cheskidov, Alexey Hou, Hedong |
| author_facet | Cheskidov, Alexey Hou, Hedong |
| contents | We prove that the unconditional uniqueness of mild solutions to the Navier-Stokes equations fails in all the Besov spaces with negative regularity index, by constructing non-trivial stationary singular solutions via convex integration. We also establish uniqueness of stationary weak solutions in an endpoint critical space. Similar results are proved for the fractional Navier-Stokes equations with arbitrarily large power of the Laplacian in both Lebesgue and Besov spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03666 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On non-uniqueness of mild solutions and stationary singular solutions to the Navier-Stokes equations Cheskidov, Alexey Hou, Hedong Analysis of PDEs 35A02, 35K55, 35Q30, 42B37, 76D05 We prove that the unconditional uniqueness of mild solutions to the Navier-Stokes equations fails in all the Besov spaces with negative regularity index, by constructing non-trivial stationary singular solutions via convex integration. We also establish uniqueness of stationary weak solutions in an endpoint critical space. Similar results are proved for the fractional Navier-Stokes equations with arbitrarily large power of the Laplacian in both Lebesgue and Besov spaces. |
| title | On non-uniqueness of mild solutions and stationary singular solutions to the Navier-Stokes equations |
| topic | Analysis of PDEs 35A02, 35K55, 35Q30, 42B37, 76D05 |
| url | https://arxiv.org/abs/2603.03666 |